Limit behavior of global attractors for the complex Ginzburg-Landau equation on infinite lattices

摘要

In this work, the authors first show the existence of global attractors A(epsilon) for the following lattice complex Ginzburg-Landau equation: [GRAPHICS] and A(0) for the following lattice Schrbdinger equation: [GRAPHICS] Then they prove that the solutions of the lattice complex Ginzburg-Landau equation converge to that of the lattice SchrOdinger equation as epsilon -> 0+. Also they prove the upper semicontinuity of A(epsilon) as epsilon -> 0+ in the sense that lim epsilon -> 0+ dist(l)(2) (A(epsilon), A(0)) = 0. (C) 2007 Elsevier Ltd. All fights reserved.